1.10: Logarithmic and quadratic composites

0606/12/O/N/17 — Question 6 · 7 marks

Functions ff and gg are defined, for x>0x > 0, by f(x)=ln⁡xf(x) = \ln x and g(x)=2x2+3g(x) = 2x^{2} + 3.
(i)
Write down the range of ff.
[1]
(ii)
Write down the range of gg.
[1]
(iii)
Find the exact value of f−1g(4)f^{-1}g(4).
[2]
(iv)
Find g−1(x)g^{-1}(x) and state its domain.
[3]